11.1 ­ Space Figures.notebook
11.1: Space Figures
April 25, 2016
Date: 4/25
A polyhedron is a three­dimensional figure,
whose surfaces are polygons.
Each polygon is a face of the polyhedron.
An edge is a segment that is formed by the
intersection of two faces.
A vertex is a point where three or more
edges intersect.
1
11.1 ­ Space Figures.notebook
April 25, 2016
Ex 1). How many vertices, edges, and faces are in each polyhedron
below:
a) vertices: _________
b) edges: __________
c) faces: __________
Name the faces:
2
11.1 ­ Space Figures.notebook
April 25, 2016
Ex 1). How many vertices, edges, and faces are in each polyhedron
below:
a) vertices: _________
b) edges: __________
c) faces: __________
Name the faces:
3
11.1 ­ Space Figures.notebook
April 25, 2016
Euler’s Formula:
Given a 3D Polyhedron:
Given a 2D Net:
4
11.1 ­ Space Figures.notebook
April 25, 2016
Ex 2). Use Euler’s formula to find the missing number.
a)
Find the number of edges:
b)
Find the number of vertices:
5
11.1 ­ Space Figures.notebook
April 25, 2016
Ex 3). Verify Euler’s Formula for each polyhedron. Draw the 3D
polyhedron and the 2D net and verify both.
a) 7 faces: 6 triangles and 1 hexagon. Find the number of vertices:
d) 5 faces: 1 rectangle and 4 triangles. Find the number of edges:
6
11.1 ­ Space Figures.notebook
April 25, 2016
c) Cube
d)
7
11.1 ­ Space Figures.notebook
April 25, 2016
Homework:
pg. 726 #1 – 15
*Include sketches for #2, 10 ­ 15
8